M. Marcolli

Publications283
h-index31
Citations4,037
Highly Influential Citations239
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Noncommutative Geometry, Quantum Fields and Motives
Quantum fields, noncommutative spaces, and motives The Riemann zeta function and noncommutative geometry Quantum statistical mechanics and Galois symmetries Endomotives, thermodynamics, and the Weil…
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Gravity and the standard model with neutrino mixing
ARASON H, 1992, PHYS REV D, V46, P3945, DOI 10.1103-PhysRevD.46.3945; Atiyah M.F., 1967, K THEORY; Avramidi I. G., 1986, THESIS MOSCOW U; BARRETT JW, HEPTH0608221; Carminati L, 1999, EUR PHYS J C,…
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From Physics to Number theory via Noncommutative Geometry
We give here a comprehensive treatment of the mathematical theory of per-turbative renormalization (in the minimal subtraction scheme with dimensional regularization), in the framework of the…
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Tensor networks, $p$-adic fields, and algebraic curves: arithmetic and the AdS$_3$/CFT$_2$ correspondence
TLDR
The result is a formulation of holography in which the bulk geometry is discrete but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization.
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Quantum fields and motives
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Dynamical Systems on Spectral Metric Spaces
Let (A,H,D) be a spectral triple, namely: A is a C^*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a…
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Cuntz–Krieger Algebras and Wavelets on Fractals
We consider representations of Cuntz–Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these…
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Equivariant Seiberg-Witten Floer Homology
This paper circulated previously in a draft version. Now, upon general request, it is about time to distribute the more detailed (and much longer) version. The main technical issues revolve around…
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Continued fractions, modular symbols, and noncommutative geometry
Abstract. Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take…
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Traces in Number Theory, Geometry and Quantum Fields
Number theory, dynamical systems, noncommutative geometry, differential geometry and quantum field theory are five areas of mathematics represented in this volume, which presents an overview of…
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